Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H

Abstract

Measuring the 2S-2P Lamb shift in a hydrogen-like muonic atom allows one to extract its nuclear charge radius with a high precision that is limited by the uncertainty in the nuclear structure corrections. The charge radius of the proton thus extracted was found to be 7-sigma away from the CODATA value, in what has become the yet unsolved "proton radius puzzle". Further experiments currently aim at the isotopes of hydrogen and helium: the precise extraction of their radii may provide a hint at the solution of the puzzle. We present the first ab initio calculation of nuclear structure corrections, including the nuclear polarization correction, to the 2S-2P transition in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H, and assess solid theoretical error bars. Our predictions reduce the uncertainty in the nuclear structure corrections to the level of a few percents and will be instrumental to the on-going ${\mu }^3$He${}^{+}$ experiment. We also support the mirror $\mu {}^3$H system as a candidate for further probing of the nucleon polarizabilities and shedding more light on the puzzle.

7 pgs., 1 fig., 1 table, plus Supplementary Materials (3 pgs., 2 tables)

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Cited by in corpus (20)

• From bound states to the continuum
• Comprehensive theory of the Lamb shift in light muonic atoms
• Ab initio calculation of nuclear structure corrections in muonic atoms
• Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift
• The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties
• Review of experimental and theoretical status of the proton radius puzzle
• Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions
• The next generation of laser spectroscopy experiments using light muonic atoms
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• Benchmark calculations of electromagnetic sum rules with a symmetry-adapted basis and hyperspherical harmonics
• Theory of the n=2 levels in muonic helium-3 ions
• Zemach moments and radii of 2,3H and 3,4He
• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
• Probing uncertainties of nuclear structure corrections in light muonic atoms
• Update on nuclear structure effects in light muonic atoms
• Two-photon exchange on neutron and the hyperfine splitting
• Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections
• Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions
• A theory vade mecum for PSI experiments
• Muonic Lithium atoms: nuclear structure corrections to the Lamb shift